(Note: these should actually be all on one line per entry, so two lines for the above.)

As always when dealing with sendmail.mc, you'll need to run the m4 processor over the file and make the hash maps. Do yourself a favour and have a Makefile to do it for you. Restart sendmail, and you should be good to go!

UPDATE: While the above is fine and works, Google's mail servers rewrite the From: address to the gmail account you use to authenticate. This is not the best solution if you want to not appear to only be able to send from gmail.com. Here are some other changes to use the ISP's mail server. (In this case I'm using netvigator.com, others should be similar.)

/etc/mail/auth/authinfo (Note that I don't need to specify the higher ports, as the ISP only accepts on port 25. The Method ("M:PLAIN") doesn't seem to be required either.